A200887 Number of 0..n arrays x(0..3) of 4 elements without any interior element greater than both neighbors.

12, 51, 144, 325, 636, 1127, 1856, 2889, 4300, 6171, 8592, 11661, 15484, 20175, 25856, 32657, 40716, 50179, 61200, 73941, 88572, 105271, 124224, 145625, 169676, 196587, 226576, 259869, 296700, 337311, 381952, 430881, 484364, 542675, 606096, 674917

Offset

1,1

Comments

Row 2 of A200886.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = (1/3)*n^4 + (7/3)*n^3 + (14/3)*n^2 + (11/3)*n + 1.

Conjectures from Colin Barker, Oct 16 2017: (Start)

G.f.: x*(12 - 9*x + 9*x^2 - 5*x^3 + x^4) / (1 - x)^5.

a(n) = (1+n)^2 * (3+5*n+n^2) / 3.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)

Example

Some solutions for n=3
..3....1....0....0....3....1....3....1....2....2....0....1....3....1....3....2
..2....1....1....0....1....1....1....0....2....3....3....0....3....3....3....0
..1....3....1....2....2....0....3....1....2....3....3....0....2....3....1....2
..1....3....0....3....3....1....3....2....2....3....2....2....2....0....2....2

Crossrefs

Sequence in context: A349860 A268351 A166776 * A236770 A334695 A115680

Adjacent sequences: A200884 A200885 A200886 * A200888 A200889 A200890

Keyword

nonn

Author

R. H. Hardin, Nov 23 2011

Status

approved